Subgroups — #27111929

Order 12032.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256998	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256259	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256251	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256084	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256048	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255784	C₂	1	2	yes	maximal, complemented
7	#20255776	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255767	C₂	1	2	yes	maximal, complemented
9	#20255745	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255232	C₂	1	2	yes	maximal, complemented
11	#20255217	C₂	1	2	yes	maximal, complemented
12	#20255206	C₂	1	1	yes	maximal, characteristic, complemented
13	#20255195	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254735	C₂	1	2	yes	maximal, complemented
15	#20254714	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254556	C₂	1	2	yes	maximal, complemented
17	#20254524	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253431	C₂	1	2	yes	maximal, complemented
19	#20253400	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253170	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15689420	C₂	1	2	yes	maximal, complemented
22	#20252499	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3515	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689858	C₂²	1	1	yes	characteristic
25	#15689833	C₂²	1	1	yes	characteristic
26	#15689830	C₂²	1	1	yes	characteristic
27	#15689819	C₂²	1	2	yes	—
28	#15689817	—	2	1	no	—
29	#15689797	—	2	2	no	—
30	#15689769	C₂²	1	2	yes	—
31	#15689761	—	2	1	no	—
32	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
33	#15689673	C₂²	1	1	yes	characteristic
34	#15689660	—	2	1	no	—
35	#15689657	C₂²	1	2	yes	—
36	#15689632	—	2	2	no	—
37	C₄×#10625350	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
39	C₄×D₄×D₄₇	—	2	1	no	—
40	#15689526	C₂²	1	1	yes	characteristic, complemented
41	#15689522	C₂²	1	2	yes	complemented
42	#15689522	C₂²	1	2	yes	complemented
43	#15689519	C₂²	1	1	yes	characteristic, complemented
44	#15689480	C₂²	1	2	yes	complemented
45	#15689480	C₂²	1	2	yes	complemented
46	#15689471	C₂²	1	1	yes	characteristic
47	#15689471	C₂²	1	1	yes	characteristic
48	#15689461	C₂²	1	1	yes	characteristic, complemented
49	#15689458	C₂²	1	2	yes	complemented
50	#15689456	C₂²	1	2	yes	complemented
51	#15689453	C₂²	1	2	yes	complemented
52	#15689447	C₂²	1	2	yes	complemented
53	#15689447	C₂²	1	2	yes	complemented
54	#15689444	C₂²	1	1	yes	characteristic, complemented
55	#15689441	C₂²	1	2	yes	—
56	#15689439	C₂²	1	2	yes	complemented
57	#15689436	C₂²	1	2	yes	—
58	#15689430	C₂²	1	2	yes	complemented
59	#15689427	C₂²	1	2	yes	complemented
60	#15689427	C₂²	1	1	yes	characteristic, complemented
61	#15689423	C₂²	1	2	yes	complemented
62	#15689420	C₂²	1	2	yes	—
63	#15689420	C₂²	1	1	yes	characteristic
64	#15689420	C₂²	1	2	yes	—
65	#15689420	C₂²	1	2	yes	—
66	#15689420	C₂²	1	2	yes	complemented
67	#15689420	C₂²	1	2	yes	complemented
68	#15689420	C₂²	1	2	yes	complemented
69	#15689420	C₂²	1	2	yes	complemented
70	#15689420	C₂²	1	2	yes	complemented
71	#15689418	C₂²	1	1	yes	characteristic, complemented
72	#15689415	C₂²	1	1	yes	characteristic, complemented
73	#15689413	C₂²	1	1	yes	characteristic, complemented
74	#15689410	C₂²	1	1	yes	characteristic
75	#15689405	C₂²	1	1	yes	characteristic, complemented
76	#15689400	C₂²	1	1	yes	characteristic
77	#15689362	C₂²	1	2	yes	complemented
78	#15689357	C₂²	1	2	yes	—
79	#15689357	C₂²	1	2	yes	complemented
80	#15689354	C₂²	1	2	yes	—
81	#15689354	C₂²	1	2	yes	complemented
82	#15689350	C₂²	1	2	yes	complemented
83	#15689345	C₂²	1	2	yes	complemented
84	#15689342	C₂²	1	1	yes	characteristic, complemented
85	#15689338	C₂²	1	2	yes	complemented
86	#15689335	C₂²	1	1	yes	characteristic
87	#15689335	C₂²	1	2	yes	complemented
88	#15689323	C₂²	1	1	yes	characteristic
89	#15689318	C₂²	1	1	yes	characteristic
90	#15689283	C₂²	1	1	yes	characteristic
91	#15689273	C₂²	1	2	yes	—
92	#15689266	C₂²	1	1	yes	characteristic
93	#15689256	C₂²	1	2	yes	—
94	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
95	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
97	C₄×#10625336	C₂²	1	1	yes	characteristic
98	C₄×#10625336	C₂²	1	2	yes	—
99	C₄×#10625336	C₂²	1	2	yes	complemented
100	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10625334	C₂²	1	2	yes	—
102	C₄×#10625334	C₂²	1	1	yes	characteristic
103	C₄×#10625334	C₂²	1	2	yes	complemented
104	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
105	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
106	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
107	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
108	#15689176	C₂²	1	1	yes	characteristic, complemented
109	#15689176	C₂²	1	2	yes	complemented
110	#15689159	C₂²	1	2	yes	complemented
111	C₂×#13093957	C₂²	1	2	yes	complemented
112	C₂×#13093955	C₂²	1	2	yes	complemented
113	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
114	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
115	#15689117	C₂²	1	2	yes	—
116	C₂×#13093944	C₂²	1	2	yes	—
117	C₂×#13093944	C₂²	1	2	yes	—
118	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
119	C₄₇×#554	C₂²	1	1	yes	characteristic
120	C₄₇×#554	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#553	C₂²	1	2	yes	complemented
122	C₄₇×#552	—	2	2	no	—
123	C₄₇×#552	—	2	1	no	—
124	C₄₇×#552	C₂²	1	2	yes	complemented
125	C₄₇×#547	—	2	1	no	—
126	C₄₇×#547	C₂²	1	1	yes	characteristic
127	C₄₇×#541	—	2	1	no	—
128	C₄₇×#539	—	2	2	no	—
129	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#529	C₂²	1	2	yes	complemented
131	C₄₇×#529	C₂²	1	1	yes	characteristic, complemented
132	C₂×#125×C₄₇	C₂²	1	2	yes	complemented
133	C₄₇×#520	—	2	1	no	—
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂²×D₁₈₈	C₂³	1	2	yes	—
138	C₂×D₄×D₄₇	—	2	1	no	—
139	C₂²×C₄×D₄₇	—	2	2	no	—
140	C₂×#10625337	C₂³	1	1	yes	characteristic
141	C₂×#10625335	C₂³	1	1	yes	characteristic
142	C₂×#10625336	C₂³	1	1	yes	characteristic
143	C₂×#10625336	C₂³	1	2	yes	—
144	C₂×#10625334	C₂³	1	1	yes	characteristic
145	C₂×#10625334	C₂³	1	2	yes	—
146	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
147	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
148	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
149	#13094024	C₂³	1	1	yes	characteristic
150	#13094021	C₂³	1	1	yes	characteristic
151	#13094019	—	2	2	no	—
152	#13094018	—	2	2	no	—
153	#13094016	C₂³	1	2	yes	—
154	#13094015	—	2	1	no	—
155	#13094013	—	2	1	no	—
156	#13094012	—	2	1	no	—
157	#13094012	C₂³	1	2	yes	—
158	#13094009	—	2	2	no	—
159	#13094009	—	2	2	no	—
160	#13094007	—	2	2	no	—
161	#13094006	—	2	2	no	—
162	#13094003	C₂³	1	2	yes	—
163	#13094002	—	2	2	no	—
164	#13094001	—	2	2	no	—
165	#13094000	—	2	1	no	—
166	#13093999	—	2	1	no	—
167	#13093998	—	2	1	no	—
168	#13093998	C₂³	1	2	yes	—
169	#13093998	C₂³	1	2	yes	—
170	#13093997	—	2	2	no	—
171	#13093996	—	2	2	no	—
172	#13093994	—	2	2	no	—
173	#13093992	—	2	2	no	—
174	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
175	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
176	C₄×D₁₈₈	—	2	2	no	—
177	C₄×D₁₈₈	—	2	1	no	—
178	C₄×D₁₈₈	—	2	2	no	—
179	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
180	C₄×D₁₈₈	C₂³	1	2	yes	—
181	C₄×D₁₈₈	C₂³	1	2	yes	—
182	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
183	C₄×D₁₈₈	C₂³	1	2	yes	—
184	D₄×Dic₄₇	—	2	1	no	—
185	#13093986	—	2	1	no	—
186	C₄×C₂²⋊D₄₇	—	2	1	no	—
187	C₄×C₂²⋊D₄₇	—	2	2	no	—
188	C₄×C₂²⋊D₄₇	—	2	1	no	—
189	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
190	#13093983	C₂³	1	1	yes	characteristic
191	#13093981	—	2	1	no	—
192	#13093981	—	2	2	no	—
193	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
194	C₄⋊C₄×D₄₇	—	2	1	no	—
195	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
196	C₂²⋊C₄×D₄₇	—	2	2	no	—
197	C₄²×D₄₇	—	2	1	no	—
198	#13093957	C₂³	1	1	yes	characteristic
199	#13093957	C₂³	1	1	yes	characteristic
200	#13093957	C₂³	1	2	yes	—
201	#13093957	C₂³	1	2	yes	—
202	#13093957	C₂³	1	2	yes	—
203	#13093957	C₂³	1	2	yes	—
204	#13093957	C₂³	1	2	yes	—
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	2	yes	—
207	#13093955	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	1	yes	characteristic
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	2	yes	—
221	#13093948	C₂³	1	1	yes	characteristic
222	#13093947	C₂³	1	1	yes	characteristic
223	#13093947	C₂³	1	1	yes	characteristic
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	2	yes	—
226	#13093945	C₂³	1	1	yes	characteristic
227	#13093945	C₂³	1	2	yes	—
228	#13093945	C₂³	1	1	yes	characteristic
229	#13093944	C₂³	1	2	yes	—
230	#13093944	C₂³	1	2	yes	—
231	#13093944	C₂³	1	2	yes	—
232	#13093944	C₂³	1	2	yes	—
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	1	yes	characteristic
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	1	yes	characteristic
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	2	yes	—
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
245	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
247	C₂×#41×C₄₇	—	2	1	no	—
248	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
249	C₄⋊Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
252	#126×C₄₇	—	2	2	no	—
253	#126×C₄₇	—	2	2	no	—
254	#126×C₄₇	—	2	2	no	—
255	#126×C₄₇	—	2	1	no	—
256	#125×C₄₇	—	2	2	no	—
257	#125×C₄₇	—	2	2	no	—
258	#125×C₄₇	—	2	1	no	—
259	#125×C₄₇	—	2	2	no	—
260	#125×C₄₇	—	2	2	no	—
261	#125×C₄₇	C₂³	1	2	yes	—
262	#125×C₄₇	C₂³	1	2	yes	—
263	#125×C₄₇	C₂³	1	1	yes	characteristic
264	#125×C₄₇	C₂³	1	2	yes	—
265	#124×C₄₇	C₂³	1	1	yes	characteristic
266	#123×C₄₇	—	2	2	no	—
267	#123×C₄₇	—	2	1	no	—
268	#123×C₄₇	—	2	2	no	—
269	#123×C₄₇	—	2	2	no	—
270	#123×C₄₇	—	2	2	no	—
271	C₂²⋊Q₈×C₄₇	—	2	1	no	—
272	C₂²⋊Q₈×C₄₇	—	2	1	no	—
273	C₂²⋊Q₈×C₄₇	—	2	1	no	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	1	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
279	#121×C₄₇	—	2	2	no	—
280	#121×C₄₇	C₂³	1	2	yes	—
281	#121×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	—	2	1	no	—
283	C₄×Q₈×C₄₇	—	2	1	no	—
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₇	—	2	1	no	—
290	C₄×D₄×C₄₇	—	2	2	no	—
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	2	no	—
293	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
294	C₄×D₄×C₄₇	D₄	1	2	yes	—
295	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₇	C₂³	1	2	yes	—
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	2	yes	—
299	#117×C₄₇	—	2	2	no	—
300	#117×C₄₇	—	2	1	no	—
301	#117×C₄₇	—	2	2	no	—
302	#117×C₄₇	D₄	1	2	yes	—
303	#117×C₄₇	D₄	1	1	yes	characteristic
304	#117×C₄₇	C₂³	1	2	yes	—
305	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
306	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
307	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
309	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂³×D₄₇	—	2	2	no	—
313	#41×C₄₇	—	2	4	no	—
314	#41×C₄₇	—	4	4	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₇	—	2	2	no	—
320	C₂×D₄×C₄₇	—	2	1	no	—
321	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
322	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	—	2	2	no	—
325	C₂²×C₄×C₄₇	—	2	2	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	2	2	no	—
328	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
331	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
334	C₂×C₂²⋊D₄₇	—	2	2	no	—
335	C₂×C₂²⋊D₄₇	—	2	1	no	—
336	C₂×C₂²⋊D₄₇	—	2	2	no	—
337	C₂²×Dic₄₇	—	2	2	no	—
338	D₄×D₄₇	—	4	4	no	—
339	#10625350	—	2	2	no	—
340	#10625350	—	4	1	no	—
341	#10625350	—	8	2	no	—
342	C₂×D₁₈₈	—	2	4	no	—
343	C₂×D₁₈₈	—	2	1	no	—
344	C₂×D₁₈₈	—	2	2	no	—
345	C₂×D₁₈₈	—	2	1	no	—
346	C₂×D₁₈₈	—	4	2	no	—
347	C₂×D₁₈₈	C₂⁴	1	2	yes	—
348	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×D₄₇	—	2	1	no	—
350	C₂×C₄×D₄₇	—	2	1	no	—
351	C₂×C₄×D₄₇	—	2	1	no	—
352	C₂×C₄×D₄₇	—	2	2	no	—
353	C₂×C₄×D₄₇	—	2	2	no	—
354	C₂×C₄×D₄₇	—	2	2	no	—
355	C₂×C₄×D₄₇	—	8	4	no	—
356	C₂×Dic₉₄	—	2	1	no	—
357	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	1	no	—
360	C₄⋊C₄×C₄₇	—	2	1	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	1	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	2	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	—	2	2	no	—
367	C₄⋊C₄×C₄₇	—	2	2	no	—
368	C₄⋊C₄×C₄₇	—	2	2	no	—
369	C₄⋊C₄×C₄₇	—	2	1	no	—
370	C₄⋊C₄×C₄₇	—	2	2	no	—
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	—	2	2	no	—
374	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
382	C₂²⋊C₄×C₄₇	—	2	2	no	—
383	C₂²⋊C₄×C₄₇	—	2	2	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₂²⋊C₄×C₄₇	—	2	1	no	—
386	C₂²⋊C₄×C₄₇	—	2	1	no	—
387	C₂²⋊C₄×C₄₇	—	2	1	no	—
388	C₂²⋊C₄×C₄₇	—	2	2	no	—
389	C₂²⋊C₄×C₄₇	—	2	2	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
394	C₄²×C₄₇	—	2	2	no	—
395	C₄²×C₄₇	—	2	2	no	—
396	C₄²×C₄₇	—	2	1	no	—
397	C₄²×C₄₇	C₂×D₄	1	2	yes	—
398	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₄₇	C₂×D₄	1	2	yes	—
401	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
402	C₄²×C₄₇	C₂⁴	1	2	yes	—
403	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
404	C₂²⋊Dic₄₇	—	2	2	no	—
405	C₂²⋊Dic₄₇	—	2	1	no	—
406	#10625337	—	4	1	no	—
407	#10625336	—	2	2	no	—
408	#10625336	—	4	2	no	—
409	#10625335	—	4	1	no	—
410	#10625334	—	2	2	no	—
411	#10625334	—	4	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	(C₂×D₄₇)⋊C₄	—	2	1	no	—
415	(C₂×D₄₇)⋊C₄	—	2	2	no	—
416	(C₂×D₄₇)⋊C₄	—	2	2	no	—
417	(C₂×D₄₇)⋊C₄	—	2	2	no	—
418	(C₂×D₄₇)⋊C₄	—	2	1	no	—
419	(C₂×D₄₇)⋊C₄	—	2	2	no	—
420	(C₂×D₄₇)⋊C₄	—	2	2	no	—
421	C₄⋊Dic₄₇	—	2	1	no	—
422	C₄⋊Dic₄₇	—	2	2	no	—
423	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
425	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	1	no	—
428	Dic₄₇⋊C₄	—	2	1	no	—
429	Dic₄₇⋊C₄	—	2	2	no	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	C₄×Dic₄₇	—	2	1	no	—
432	C₄×Dic₄₇	—	2	1	no	—
433	C₄×Dic₄₇	—	2	1	no	—
434	C₂×C₄₇⋊C₈	—	4	2	no	—
435	C₂×C₄₇⋊C₈	—	4	2	no	—
436	C₂×C₄₇⋊C₈	—	4	2	no	—
437	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
438	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
439	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
441	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
442	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
443	C₂³×C₄₇	—	2	1	no	—
444	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
445	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
446	C₂²×D₄₇	—	2	1	no	—
447	C₂²×D₄₇	—	2	2	no	—
448	C₂²×D₄₇	—	4	4	no	—
449	C₂²×D₄₇	—	4	4	no	—
450	C₂²×D₄₇	—	8	2	no	—
451	Q₈×C₄₇	—	2	2	no	—
452	Q₈×C₄₇	—	2	1	no	—
453	Q₈×C₄₇	—	2	1	no	—
454	Q₈×C₄₇	—	4	2	no	—
455	Q₈×C₄₇	—	8	1	no	—
456	D₄×C₄₇	—	2	4	no	—
457	D₄×C₄₇	—	2	1	no	—
458	D₄×C₄₇	—	2	1	no	—
459	D₄×C₄₇	—	4	4	no	—
460	D₄×C₄₇	—	8	1	no	—
461	D₄×C₄₇	#135	1	4	yes	—
462	C₂×C₄×C₄₇	—	2	4	no	—
463	C₂×C₄×C₄₇	—	2	2	no	—
464	C₂×C₄×C₄₇	—	2	2	no	—
465	C₂×C₄×C₄₇	—	2	1	no	—
466	C₂×C₄×C₄₇	—	2	2	no	—
467	C₂×C₄×C₄₇	—	2	1	no	—
468	C₂×C₄×C₄₇	—	2	1	no	—
469	C₂×C₄×C₄₇	—	2	2	no	—
470	C₂×C₄×C₄₇	—	2	2	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	4	2	no	—
474	C₂×C₄×C₄₇	—	4	1	no	—
475	C₂×C₄×C₄₇	—	4	4	no	—
476	C₂×C₄×C₄₇	—	4	2	no	—
477	C₂×C₄×C₄₇	—	8	2	no	—
478	C₂×C₄×C₄₇	—	8	2	no	—
479	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
488	C₂²⋊D₄₇	—	4	2	no	—
489	C₂²⋊D₄₇	—	4	4	no	—
490	C₂²⋊D₄₇	—	8	2	no	—
491	C₂×Dic₄₇	—	2	1	no	—
492	C₂×Dic₄₇	—	2	1	no	—
493	C₂×Dic₄₇	—	2	1	no	—
494	C₂×Dic₄₇	—	2	2	no	—
495	C₂×Dic₄₇	—	8	2	no	—
496	D₁₈₈	—	2	2	no	—
497	D₁₈₈	—	2	1	no	—
498	D₁₈₈	—	2	2	no	—
499	D₁₈₈	—	4	4	no	—
500	D₁₈₈	—	4	2	no	—
501	D₁₈₈	—	8	1	no	—
502	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
503	C₄×D₄₇	—	4	2	no	—
504	C₄×D₄₇	—	4	2	no	—
505	C₄×D₄₇	—	4	4	no	—
506	C₄×D₄₇	—	4	2	no	—
507	C₄×D₄₇	—	8	2	no	—
508	C₄×D₄₇	—	8	2	no	—
509	Dic₉₄	—	2	1	no	—
510	Dic₉₄	—	2	1	no	—
511	Dic₉₄	—	8	1	no	—
512	C₄₇⋊C₈	—	2	1	no	—
513	C₄₇⋊C₈	—	2	1	no	—
514	C₄₇⋊C₈	—	2	2	no	—
515	C₄₇⋊C₈	—	2	1	no	—
516	C₄₇⋊C₈	—	2	2	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	#62103	—	47	1	no	maximal, Sylow
519	C₂²×C₄₇	—	2	2	no	—
520	C₂²×C₄₇	—	2	2	no	—
521	C₂²×C₄₇	—	2	1	no	—
522	C₂²×C₄₇	—	2	1	no	—
523	C₂²×C₄₇	—	2	1	no	—
524	C₂²×C₄₇	—	4	1	no	—
525	C₂²×C₄₇	—	4	1	no	—
526	C₂²×C₄₇	—	4	1	no	—
527	C₂²×C₄₇	C₂×#135	1	4	yes	—
528	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
529	C₂×D₄₇	—	2	2	no	—
530	C₂×D₄₇	—	4	1	no	—
531	C₂×D₄₇	—	4	1	no	—
532	C₂×D₄₇	—	4	2	no	—
533	C₂×D₄₇	—	4	2	no	—
534	C₂×D₄₇	—	4	2	no	—
535	C₂×D₄₇	—	8	8	no	—
536	C₄×C₄₇	—	2	1	no	—
537	C₄×C₄₇	—	2	1	no	—
538	C₄×C₄₇	—	2	2	no	—
539	C₄×C₄₇	—	2	1	no	—
540	C₄×C₄₇	—	2	2	no	—
541	C₄×C₄₇	—	2	1	no	—
542	C₄×C₄₇	—	2	2	no	—
543	C₄×C₄₇	—	4	1	no	—
544	C₄×C₄₇	—	4	2	no	—
545	C₄×C₄₇	—	4	1	no	—
546	C₄×C₄₇	—	4	1	no	—
547	C₄×C₄₇	—	4	2	no	—
548	C₄×C₄₇	C₂×#135	1	2	yes	—
549	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	C₄×C₄₇	#585	1	1	yes	characteristic
551	Dic₄₇	—	4	2	no	—
552	Dic₄₇	—	4	1	no	—
553	Dic₄₇	—	4	1	no	—
554	Dic₄₇	—	4	1	no	—
555	#3515	D₄₇	1	1	yes	characteristic, complemented
556	#3481	—	47	1	no	—
557	#3381	—	47	1	no	—
558	#3380	—	47	1	no	—
559	#3365	—	47	1	no	—
560	#3361	—	47	1	no	—
561	#3339	—	47	2	no	—
562	#3338	—	47	1	no	—
563	#3337	—	47	2	no	—
564	#3335	—	47	1	no	—
565	#3297	—	47	2	no	—
566	#3296	—	47	2	no	—
567	#3295	—	47	1	no	—
568	#3294	—	47	1	no	—
569	#3250	—	47	2	no	—
570	#3247	—	47	1	no	—
571	#3232	—	47	2	no	—
572	#3228	—	47	1	no	—
573	#3105	—	47	2	no	—
574	#3102	—	47	1	no	—
575	#3076	—	47	1	no	—
576	C₂×#478	—	47	2	no	—
577	#2988	—	47	1	no	—
578	C₂×C₄₇	—	2	4	no	—
579	C₂×C₄₇	—	4	1	no	—
580	C₂×C₄₇	—	8	1	no	—
581	C₂×C₄₇	#3489	1	1	yes	characteristic
582	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
583	C₂×C₄₇	#3585	1	1	yes	characteristic
584	D₄₇	—	4	2	no	—
585	D₄₇	—	8	2	no	—
586	#559	—	47	1	no	—
587	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
588	#554	—	47	1	no	—
589	#554	—	47	1	no	—
590	#554	C₂×D₄₇	1	1	yes	characteristic
591	#554	C₂×D₄₇	1	1	yes	characteristic, complemented
592	#553	—	47	2	no	—
593	#553	—	94	1	no	—
594	#553	C₂×D₄₇	1	2	yes	complemented
595	#552	—	2	2	no	—
596	#552	—	2	1	no	—
597	#552	C₂×D₄₇	1	2	yes	complemented
598	#551	—	94	2	no	—
599	#547	—	2	1	no	—
600	#547	C₂×D₄₇	1	1	yes	characteristic
601	#546	—	47	2	no	—
602	#546	—	94	1	no	—
603	D₄²	—	47	1	no	—
604	#541	—	2	1	no	—
605	#539	—	2	2	no	—
606	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
607	#532	—	47	1	no	—
608	#529	—	47	2	no	—
609	#529	—	94	1	no	—
610	#529	C₂×D₄₇	1	1	yes	characteristic, complemented
611	#529	C₂×D₄₇	1	2	yes	complemented
612	C₂×#125	C₂×D₄₇	1	2	yes	complemented
613	#525	—	94	2	no	—
614	#520	—	2	1	no	—
615	C₄×#41	—	47	1	no	—
616	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
617	C₂×C₄×D₄	—	47	2	no	—
618	C₂×C₄×D₄	—	94	1	no	—
619	#500	—	47	1	no	—
620	#499	—	47	2	no	—
621	#499	—	47	2	no	—
622	#498	—	47	1	no	—
623	#488	—	47	2	no	—
624	#488	—	47	2	no	—
625	#486	—	47	1	no	—
626	#486	—	47	1	no	—
627	#485	—	47	1	no	—
628	#484	—	47	2	no	—
629	#484	—	47	2	no	—
630	#483	—	47	2	no	—
631	#482	—	47	1	no	—
632	#482	—	47	2	no	—
633	#482	—	47	2	no	—
634	#481	—	47	2	no	—
635	#481	—	47	2	no	—
636	#480	—	47	2	no	—
637	#479	—	47	2	no	—
638	#479	—	47	1	no	—
639	#479	—	47	2	no	—
640	#478	—	47	1	no	—
641	#478	—	47	2	no	—
642	#478	—	47	2	no	—
643	#478	—	47	2	no	—
644	#478	—	47	2	no	—
645	#478	—	47	2	no	—
646	#478	—	47	2	no	—
647	#478	—	47	2	no	—
648	#478	—	47	2	no	—
649	#478	—	47	2	no	—
650	#477	—	47	1	no	—
651	#477	—	47	1	no	—
652	#476	—	47	1	no	—
653	#476	—	47	1	no	—
654	#475	—	47	1	no	—
655	#474	—	47	1	no	—
656	#467	—	47	2	no	—
657	#466	—	47	2	no	—
658	#466	—	47	2	no	—
659	#465	—	47	2	no	—
660	#465	—	47	2	no	—
661	#465	—	47	2	no	—
662	#464	—	47	1	no	—
663	#464	—	47	2	no	—
664	#463	—	47	1	no	—
665	#463	—	47	2	no	—
666	#463	—	47	2	no	—
667	#460	—	47	1	no	—
668	#459	—	47	1	no	—
669	#452	—	47	1	no	—
670	#450	—	47	2	no	—
671	#449	—	47	1	no	—
672	#447	—	47	2	no	—
673	C₈×Q₈	—	47	1	no	—
674	C₈×Q₈	—	47	1	no	—
675	C₄×Q₁₆	—	47	1	no	—
676	C₄×SD₁₆	—	47	2	no	—
677	C₄×SD₁₆	—	47	1	no	—
678	C₄×SD₁₆	—	47	2	no	—
679	C₄×SD₁₆	—	47	1	no	—
680	C₄×D₈	—	47	2	no	—
681	C₄×D₈	—	47	1	no	—
682	C₄×D₈	—	47	2	no	—
683	C₈×D₄	—	47	1	no	—
684	C₈×D₄	—	47	2	no	—
685	C₈×D₄	—	47	1	no	—
686	C₈×D₄	—	47	2	no	—
687	#431	—	47	1	no	—
688	#431	—	47	2	no	—
689	#427	—	47	2	no	—
690	C₂×#107	—	47	2	no	—
691	C₂×#106	—	47	2	no	—
692	C₂×C₄⋊C₈	—	47	2	no	—
693	C₂×C₄⋊C₈	—	47	1	no	—
694	#416	—	47	2	no	—
695	C₂×#102	—	47	2	no	—
696	C₂×#102	—	47	2	no	—
697	C₄₇	#62103	1	1	yes	characteristic, complemented, Sylow
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	47	1	no	—
700	C₂×#41	—	94	1	no	—
701	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
702	C₂²×D₄	—	47	2	no	—
703	C₂²×D₄	—	94	1	no	—
704	C₂³×C₄	—	94	2	no	—
705	C₂×Q₁₆	—	47	1	no	—
706	C₂×SD₁₆	—	47	1	no	—
707	C₂×SD₁₆	—	47	2	no	—
708	C₂×SD₁₆	—	47	1	no	—
709	C₂×D₈	—	47	1	no	—
710	C₂×D₈	—	47	2	no	—
711	C₂²×C₈	—	47	2	no	—
712	C₂²×C₈	—	47	2	no	—
713	C₂²×C₈	—	47	2	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	47	1	no	—
716	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
717	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
718	#127	—	47	1	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	1	no	—
723	#126	—	94	2	no	—
724	#126	—	94	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	47	2	no	—
731	#125	—	94	1	no	—
732	#125	C₂²×D₄₇	1	1	yes	characteristic
733	#125	C₂²×D₄₇	1	2	yes	—
734	#125	C₂²×D₄₇	1	2	yes	—
735	#125	C₂²×D₄₇	1	2	yes	—
736	#124	—	47	2	no	—
737	#124	—	94	1	no	—
738	#124	—	94	1	no	—
739	#124	C₂²×D₄₇	1	1	yes	characteristic
740	#123	—	2	2	no	—
741	#123	—	2	1	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	94	2	no	—
746	#123	—	94	2	no	—
747	#123	—	94	2	no	—
748	#123	—	94	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	47	2	no	—
756	C₂²⋊Q₈	—	94	1	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	C₂²⋊Q₈	—	94	2	no	—
759	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
761	#121	—	2	2	no	—
762	#121	—	47	2	no	—
763	#121	—	47	2	no	—
764	#121	—	94	2	no	—
765	#121	—	94	1	no	—
766	#121	—	94	1	no	—
767	#121	—	94	2	no	—
768	#121	C₂²×D₄₇	1	2	yes	—
769	#121	C₂²×D₄₇	1	1	yes	characteristic
770	#120	—	94	2	no	—
771	#120	—	94	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	47	1	no	—
776	C₄×Q₈	—	47	1	no	—
777	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
778	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
779	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
780	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	47	1	no	—
786	C₄×D₄	—	47	2	no	—
787	C₄×D₄	—	47	2	no	—
788	C₄×D₄	—	47	2	no	—
789	C₄×D₄	—	47	1	no	—
790	C₄×D₄	—	94	1	no	—
791	C₄×D₄	—	94	2	no	—
792	C₄×D₄	—	94	1	no	—
793	C₄×D₄	—	94	1	no	—
794	C₄×D₄	—	94	1	no	—
795	C₄×D₄	—	94	2	no	—
796	C₄×D₄	—	94	2	no	—
797	C₄×D₄	—	94	2	no	—
798	C₄×D₄	—	94	1	no	—
799	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
800	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
801	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
802	C₄×D₄	C₂²×D₄₇	1	2	yes	—
803	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
804	C₄×D₄	C₂²×D₄₇	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	47	1	no	—
809	#117	—	94	1	no	—
810	#117	—	94	2	no	—
811	#117	C₂²⋊D₄₇	1	2	yes	—
812	#117	C₂²⋊D₄₇	1	1	yes	characteristic
813	#117	C₂²×D₄₇	1	2	yes	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	47	2	no	—
818	C₂×C₄⋊C₄	—	94	1	no	—
819	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
820	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
821	C₂×C₂²⋊C₄	—	94	2	no	—
822	C₂×C₂²⋊C₄	—	94	2	no	—
823	C₂×C₄²	—	94	1	no	—
824	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
825	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
826	#107	—	47	1	no	—
827	#107	—	47	2	no	—
828	#107	—	47	2	no	—
829	#107	—	47	2	no	—
830	#107	—	47	2	no	—
831	#107	—	47	2	no	—
832	#107	—	47	1	no	—
833	#106	—	47	1	no	—
834	#106	—	47	2	no	—
835	#106	—	47	2	no	—
836	#106	—	47	2	no	—
837	#106	—	47	2	no	—
838	#106	—	47	2	no	—
839	#106	—	47	1	no	—
840	C₄⋊C₈	—	47	2	no	—
841	C₄⋊C₈	—	47	1	no	—
842	C₄⋊C₈	—	47	1	no	—
843	C₄⋊C₈	—	47	1	no	—
844	C₄⋊C₈	—	47	2	no	—
845	C₄⋊C₈	—	47	2	no	—
846	C₄⋊C₈	—	47	1	no	—
847	#103	—	47	1	no	—
848	#103	—	47	2	no	—
849	#103	—	47	1	no	—
850	#103	—	47	2	no	—
851	#103	—	47	2	no	—
852	#103	—	47	1	no	—
853	#103	—	47	1	no	—
854	#102	—	47	1	no	—
855	#102	—	47	2	no	—
856	#102	—	47	1	no	—
857	#102	—	47	1	no	—
858	#102	—	47	1	no	—
859	#102	—	47	2	no	—
860	#102	—	47	2	no	—
861	#102	—	47	2	no	—
862	#102	—	47	2	no	—
863	#102	—	47	2	no	—
864	#102	—	47	2	no	—
865	#102	—	47	2	no	—
866	#102	—	47	2	no	—
867	C₂²⋊C₈	—	47	2	no	—
868	C₂²⋊C₈	—	47	1	no	—
869	C₂²⋊C₈	—	47	2	no	—
870	C₂²⋊C₈	—	47	1	no	—
871	C₄×C₈	—	47	2	no	—
872	C₄×C₈	—	47	2	no	—
873	C₄×C₈	—	47	1	no	—
874	C₄×C₈	—	47	1	no	—
875	C₂⁴	—	94	2	no	—
876	#41	—	2	4	no	—
877	#41	—	4	4	no	—
878	#41	—	94	2	no	—
879	#41	—	376	2	no	—
880	#41	—	188	1	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	47	1	no	—
884	C₂×Q₈	—	94	1	no	—
885	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
886	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	47	1	no	—
890	C₂×D₄	—	47	2	no	—
891	C₂×D₄	—	94	4	no	—
892	C₂×D₄	—	94	2	no	—
893	C₂×D₄	—	94	1	no	—
894	C₂×D₄	—	94	2	no	—
895	C₂×D₄	—	94	1	no	—
896	C₂×D₄	—	94	2	no	—
897	C₂×D₄	—	94	1	no	—
898	C₂×D₄	—	188	2	no	—
899	C₂×D₄	—	188	4	no	—
900	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
901	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
902	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	94	2	no	—
908	C₂²×C₄	—	94	2	no	—
909	C₂²×C₄	—	94	2	no	—
910	C₂²×C₄	—	94	1	no	—
911	C₂²×C₄	—	94	1	no	—
912	C₂²×C₄	—	94	1	no	—
913	C₂²×C₄	—	94	2	no	—
914	C₂²×C₄	—	376	4	no	—
915	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
916	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
917	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
918	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
919	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
920	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
921	Q₁₆	—	188	1	no	—
922	SD₁₆	—	94	2	no	—
923	SD₁₆	—	188	1	no	—
924	SD₁₆	—	188	2	no	—
925	D₈	—	94	2	no	—
926	D₈	—	188	2	no	—
927	C₂×C₈	—	47	1	no	—
928	C₂×C₈	—	47	1	no	—
929	C₂×C₈	—	47	1	no	—
930	C₂×C₈	—	47	1	no	—
931	C₂×C₈	—	47	2	no	—
932	C₂×C₈	—	47	2	no	—
933	C₂×C₈	—	188	2	no	—
934	C₂×C₈	—	188	2	no	—
935	C₂×C₈	—	188	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	47	1	no	—
953	C₄⋊C₄	—	47	2	no	—
954	C₄⋊C₄	—	47	1	no	—
955	C₄⋊C₄	—	94	2	no	—
956	C₄⋊C₄	—	94	1	no	—
957	C₄⋊C₄	—	94	1	no	—
958	C₄⋊C₄	—	94	2	no	—
959	C₄⋊C₄	—	94	2	no	—
960	C₄⋊C₄	—	94	2	no	—
961	C₄⋊C₄	—	94	1	no	—
962	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
963	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
964	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
965	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
966	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
968	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
969	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	94	2	no	—
980	C₂²⋊C₄	—	94	1	no	—
981	C₂²⋊C₄	—	94	1	no	—
982	C₂²⋊C₄	—	94	2	no	—
983	C₂²⋊C₄	—	94	2	no	—
984	C₂²⋊C₄	—	94	2	no	—
985	C₂²⋊C₄	—	94	2	no	—
986	C₂²⋊C₄	—	94	2	no	—
987	C₂²⋊C₄	—	94	1	no	—
988	C₂²⋊C₄	—	94	2	no	—
989	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
991	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
992	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	94	1	no	—
997	C₄²	—	94	1	no	—
998	C₄²	—	94	1	no	—
999	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1000	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1001	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1002	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
1003	C₄²	C₂³×D₄₇	1	2	yes	—
1004	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1005	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	94	1	no	—
1008	C₂³	—	94	2	no	—
1009	C₂³	—	376	2	no	—
1010	C₂³	—	188	4	no	—
1011	C₂³	—	188	4	no	—
1012	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1013	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	4	2	no	—
1018	Q₈	—	8	1	no	—
1019	Q₈	—	94	1	no	—
1020	Q₈	—	94	1	no	—
1021	Q₈	—	376	1	no	—
1022	D₄	—	2	4	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	47	2	no	—
1028	D₄	—	94	2	no	—
1029	D₄	—	94	1	no	—
1030	D₄	—	94	2	no	—
1031	D₄	—	376	1	no	—
1032	D₄	—	376	2	no	—
1033	D₄	—	188	4	no	—
1034	D₄	—	188	2	no	—
1035	D₄	—	188	4	no	—
1036	D₄	—	188	2	no	—
1037	D₄	#13094044	1	4	yes	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	1	no	—
1051	C₂×C₄	—	4	4	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	94	1	no	—
1056	C₂×C₄	—	94	1	no	—
1057	C₂×C₄	—	94	1	no	—
1058	C₂×C₄	—	94	2	no	—
1059	C₂×C₄	—	376	2	no	—
1060	C₂×C₄	—	376	2	no	—
1061	C₂×C₄	—	376	2	no	—
1062	C₂×C₄	—	188	2	no	—
1063	C₂×C₄	—	188	2	no	—
1064	C₂×C₄	—	188	4	no	—
1065	C₂×C₄	—	188	2	no	—
1066	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1067	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1068	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1069	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1070	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1071	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1072	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1073	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1074	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1075	C₈	—	94	1	no	—
1076	C₈	—	94	1	no	—
1077	C₈	—	94	2	no	—
1078	C₈	—	94	1	no	—
1079	C₈	—	94	2	no	—
1080	C₈	—	94	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	94	2	no	—
1090	C₂²	—	376	8	no	—
1091	C₂²	—	188	2	no	—
1092	C₂²	—	188	2	no	—
1093	C₂²	—	188	2	no	—
1094	C₂²	—	188	1	no	—
1095	C₂²	—	188	1	no	—
1096	C₂²	C₂×#13094044	1	4	yes	—
1097	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	188	1	no	—
1111	C₄	—	188	1	no	—
1112	C₄	—	188	1	no	—
1113	C₄	—	188	2	no	—
1114	C₄	C₂×#13094044	1	2	yes	—
1115	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1116	C₄	#15689960	1	1	yes	characteristic
1117	C₂	—	2	4	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	8	1	no	—
1120	C₂	—	376	2	no	—
1121	C₂	—	188	2	no	—
1122	C₂	#20257061	1	1	yes	characteristic
1123	C₂	C₂²×#13094044	1	1	yes	characteristic
1124	C₂	#20258167	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3515	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3515	D₄₇
hypocenter	C₄₇	#62103
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3515

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20256998	C₂	semidirect
2. #20256259	C₂	semidirect
3. #20256251	C₂	semidirect
4. #20256084	C₂	semidirect
5. #20256048	C₂	semidirect
6. #20255784	C₂	semidirect
7. #20255776	C₂	semidirect
8. #20255767	C₂	semidirect
9. #20255745	C₂	semidirect
10. #20255232	C₂	semidirect
11. #20255217	C₂	semidirect
12. #20255206	C₂	semidirect
13. #20255195	C₂	semidirect
14. #20254735	C₂	semidirect
15. #20254714	C₂	semidirect
16. #20254556	C₂	semidirect
17. #20254524	C₂	semidirect
18. #20253431	C₂	semidirect
19. #20253400	C₂	semidirect
20. #20253170	C₂	semidirect
21. C₂×#15689420	C₂	semidirect
22. #20252499	C₂	semidirect
23. C₄₇×#3515	C₂	semidirect
40. #15689526	C₂²	semidirect
41. #15689522	C₂²	semidirect
42. #15689522	C₂²	semidirect
43. #15689519	C₂²	semidirect
44. #15689480	C₂²	semidirect
45. #15689480	C₂²	semidirect
48. #15689461	C₂²	semidirect
49. #15689458	C₂²	semidirect
50. #15689456	C₂²	semidirect
51. #15689453	C₂²	semidirect
52. #15689447	C₂²	semidirect
53. #15689447	C₂²	semidirect
54. #15689444	C₂²	semidirect
56. #15689439	C₂²	semidirect
58. #15689430	C₂²	semidirect
59. #15689427	C₂²	semidirect
60. #15689427	C₂²	semidirect
61. #15689423	C₂²	semidirect
66. #15689420	C₂²	semidirect
67. #15689420	C₂²	semidirect
68. #15689420	C₂²	semidirect
69. #15689420	C₂²	semidirect
70. #15689420	C₂²	semidirect
71. #15689418	C₂²	semidirect
72. #15689415	C₂²	semidirect
73. #15689413	C₂²	semidirect
75. #15689405	C₂²	semidirect
77. #15689362	C₂²	semidirect
79. #15689357	C₂²	semidirect
81. #15689354	C₂²	semidirect
82. #15689350	C₂²	semidirect
83. #15689345	C₂²	semidirect
84. #15689342	C₂²	semidirect
85. #15689338	C₂²	semidirect
87. #15689335	C₂²	semidirect
94. Q₈×C₄₇⋊C₈	C₂²	semidirect
95. Q₈×C₄₇⋊C₈	C₂²	semidirect
96. C₄×#10625337	C₂²	semidirect
99. C₄×#10625336	C₂²	semidirect
100. C₄×#10625335	C₂²	semidirect
103. C₄×#10625334	C₂²	semidirect
106. D₄×C₄₇⋊C₈	C₂²	semidirect
107. D₄×C₄₇⋊C₈	C₂²	semidirect
108. #15689176	C₂²	semidirect
109. #15689176	C₂²	semidirect
110. #15689159	C₂²	semidirect
111. C₂×#13093957	C₂²	semidirect
112. C₂×#13093955	C₂²	semidirect
113. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
114. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
118. C₄₇×#557	C₂²	semidirect
120. C₄₇×#554	C₂²	semidirect
121. C₄₇×#553	C₂²	semidirect
124. C₄₇×#552	C₂²	semidirect
129. C₄₇×#533	C₂²	semidirect
130. C₄₇×#529	C₂²	semidirect
131. C₄₇×#529	C₂²	semidirect
132. C₂×#125×C₄₇	C₂²	semidirect
555. #3515	D₄₇	semidirect
587. #557	C₂×D₄₇	semidirect
591. #554	C₂×D₄₇	semidirect
594. #553	C₂×D₄₇	semidirect
597. #552	C₂×D₄₇	semidirect
606. #533	C₂×D₄₇	semidirect
610. #529	C₂×D₄₇	semidirect
611. #529	C₂×D₄₇	semidirect
612. C₂×#125	C₂×D₄₇	semidirect
697. C₄₇	#62103	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20256998	2
#20256259	2
#20256251	2
#20256084	2
#20256048	2
#20255784	2
#20255776	2
#20255767	2
#20255745	2
#20255232	2
#20255217	2
#20255206	2
#20255195	2
#20254735	2
#20254714	2
#20254556	2
#20254524	2
#20253431	2
#20253400	2
#20253170	2
C₂×#15689420	2
#20252499	2
C₄₇×#3515	2
#62103	47